Financial services, computing and IT, transport and communication, and business to business services showed the strongest growth. Photograph: High Level/Rex

Britain's services sector maintained its year-long surge in output during December as businesses reported a rise in confidence for the coming year.

The rise in activity was a little weaker than the previous month and the pace of growth was slowest since June, but still outstripped the eurozone average and especially France, which suffered a second successive month of falling services output – and at an accelerating rate.

In the UK slower growth in December reflected a general wilting across the major business sectors in the last month of 2013 with the exception of construction. Figures last week revealed that manufacturing growth dipped, though like services remained at historic highs.

The Markit/CIPS purchasing managers index (PMI) found that after accounting for seasonal factors, the headline business activity index registered a level of 58.8, down from 60 in November.

Optimism among the survey panel was at its highest since the coalition government came to power in March 2010, with businesses indicating they plan to increase investment in capacity, new products and marketing during 2014.

Markit said growth was driven by a rise in new business, which has risen continuously throughout 2013. It said the average growth rate in the final quarter of the year was the best in the survey history, despite December registering the weakest increase in new work for three months.

Chris Williamson, the firm's chief economist, said: "Service providers ended 2013 in a buoyant mood. Although growth of business activity slowed, it's come down from super-strong levels and the pace of expansion remains elevated. Combined with still-strong growth in manufacturing and services, the PMI surveys suggest that the pace of economic growth will have accelerated in the fourth quarter from the 0.8% expansion seen in the third quarter.

"If the buoyancy of the surveys in the fourth quarter is borne out by the official data, the economy will have grown by 1.9% over the course of 2013; which would be the best we've seen since 2007."

James Knightley, an economist at ING Financial Markets, said: "With new orders remaining very firm in general and the weekend's slew of business surveys, including the Deloitte CFO survey, suggesting that large corporates are clearly moving into expansion mode, this indicates to us that momentum remains strong as we start 2014."

In the eurozone, Germany, Spain and Ireland pushed the services PMI to 52.1 in December. Germany moderated to 53.5 after reaching a 10-month high of 55.7 in November. Spain picked up to 54.2 from 51.5 and Ireland saw its services sector expand at the fastest rate for nearly seven years, up to 61.8 from 57.1. But Italy and France suffered a second month of contraction, down to a six-month low of 47.8 from 48.5.

Howard Archer, chief European economist at IHS Global Insight, said: "This reinforces concern over the underlying state of the French economy which suffered renewed GDP contraction in the third quarter. It also raises doubts as to whether Italy was finally able to return to expansion in the fourth quarter of 2013 after GDP stabilised in the third quarter and puts a dampener on growth hopes for 2014."